Coupled grooving and migration of inclined grain boundaries: Regime II

Abstract

This work studies the coupled grooving and migration of an initially straight, inclined grain boundary ending at a horizontal free surface with an inclination angle β⪡1. The coupled motion is separated into two time regimes. In Regime I, the grain boundary turns vertically at the groove root. In Regime II, the turning relaxes following two different paths depending on σ/ β, where σ is the supplementary dihedral angle. For β> σ/6, the groove root positions (x 0 ,y 0 )∼(t 1 /2 , t 1 /6 ) as time t→∞, whereas for β<σ /6 , (x 0 , y 0 )∼(t 1 /4 , t 1 /4 ) as t→∞. These results come from asymptotic expansions and agree with a finite-difference solution of the coupled equations. They show that the grain boundary is never pinned. The asymptotic solutions also apply to the Sun–Bauer method of measuring mobility, and predict grain-boundary profiles that agree better with experiments.